@article{ajma2013112,
author={AUTHOR = {Provatidis, Christopher and Markakis, Emmanuel and Markakis, Nikiforos},
title={Rule of Thumb Bounds in Goldbach¡¯s Conjecture},
journal={American Journal of Mathematical Analysis},
volume={1},
number={1},
pages={8--13},
year={2013},
url={http://pubs.sciepub.com/ajma/1/1/2},
abstract={This paper determines proper factors for old and novel logarithmic functions previously used in asymptotic formulas, to make them conservative lower bounds for the ¡°thumb-of-rule¡± estimation of the number of representations of an even number 2n as a sum of two odd primes (Goldbach¡¯s conjecture). Numerical experiments up to 2n = 500,000 show that, in the graph of the number of prime-pairs versus 2n, the ratio of the ordinate of lowest ¡°cloud¡± points over the aforementioned functions tends asymptotically to values between 0.61 and 0.74. One of the three formulas proposed takes the simple form 4n/[3(lnn)<SUP>2</SUP>], which is a conservative lower bound for the number of representations of an even number 2n as a sum of two odd primes.},
doi={10.12691/ajma-1-1-2}
publisher={Science and Education Publishing}
}